cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A266296 Decimal expansion of a number close to 24, related to the Ramanujan number e^(Pi*sqrt(163)).

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%I A266296 #28 Feb 16 2025 08:33:28
%S A266296 2,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,1,2,7,8,7,3,8,6,1,4,1,1,2,0,7,
%T A266296 5,0,6,3,5,1,1,5,7,2,8,9,0,7,2,5,7,7,2,6,4,9,5,5,4,3,5,0,9,9,5,1,2,3,
%U A266296 4,5,2,7,1,7,9,8,6,3,2,0,3,3,8,0,9,1,3,0,5,8,5,8,5,9,3,7,4,9,3,5,6,5,5,2,9
%N A266296 Decimal expansion of a number close to 24, related to the Ramanujan number e^(Pi*sqrt(163)).
%H A266296 Tito Piezas III <a href="https://sites.google.com/site/tpiezas/Home">The Ramanujan pages</a>, see section 22.
%H A266296 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/AlmostInteger.html">Almost Integer</a>
%F A266296 x^24 - e^(Pi*sqrt(163)), where x is the real root of x^3 - 6x^2 + 4x - 2.
%e A266296 24.00000000000000105127873861411207506351157289072577264955435...
%t A266296 QP = QPochhammer; r4A[tau_] := With[{q = Exp[2 I Pi tau]}, (1/q) (QP[q^2]^2/(QP[q] QP[q^4]))^24]; RealDigits[r4A[(1/2) Sqrt[-163]] - Exp[Pi Sqrt[163]], 10, 105][[1]]
%t A266296 (* or: *)
%t A266296 x = Root[#^3 - 6#^2 + 4# - 2&, 1]; RealDigits[x^24 - Exp[Pi Sqrt[ 163]], 10, 105][[1]]
%Y A266296 Cf. A060295, A097340, A114609, A114610.
%K A266296 nonn,cons
%O A266296 2,1
%A A266296 _Jean-François Alcover_, Mar 13 2016